Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among 100 students, what is the probability that: (i) you both enter the same section? (ii) you both enter the different section?
Given:
Section A contains 40 students
Section B contains 60 students
It is told that you and your friend are among 100 students
We need to find:
i. You both enter the same section
ii. You both enter the different section
⇒ P(Ssame) = P(You and your friend enter same section)
This happens only in the case if you and your friend belongs to either section A or section B.
⇒ P(Ssame) = P(Both belongs to section A) + P(Both belongs to section B)
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ P(Sdiff) = P(You and your friend enter different section)
This happens only in the case if you belongs to A and your friend belongs to section B.
⇒ P(Sdiff) = 1-P(Both belongs to same section)
⇒ P(Sdiff) = 1-P(Ssame)
⇒ 
⇒ 
∴ The required probabilities are 
.